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A087648 a(n) = (1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)). 4
1, 3, 9, 31, 120, 514, 2407, 12205, 66491, 386699, 2388096, 15589732, 107165081, 773106715, 5836100685, 45981026703, 377230766908, 3215977070706, 28437411817135, 260380616093533, 2464930698184351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sum of last number in all set partitions of n+1. E.g. The set partitions of 3 are {1,1,1}, {1,1,2}, {1,2,1}, {1,2,2} and {1,2,3}, so a(2) = 1+2+1+2+3 = 9. - Franklin T. Adams-Watters, Jun 07 2006

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

MATHEMATICA

f[0]=1; f[n_] := Sum[ StirlingS2[n, k]*Binomial[k+2, k ], {k, 1, n}]; Table[ f[n], {n, 0, 20}] (* Zerinvary Lajos, Mar 31 2007 *)

PROG

(MAGMA) [(1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)) : n in [0..30]]; // Vincenzo Librandi, Nov 13 2011

CROSSREFS

Cf. A000110, A035098, A059606.

Main diagonal of A120057, row sums of A120095.

Column 1 of array in A322770.

Sequence in context: A073724 A151037 A066571 * A086616 A040027 A182968

Adjacent sequences:  A087645 A087646 A087647 * A087649 A087650 A087651

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Sep 23 2003

STATUS

approved

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Last modified February 19 20:17 EST 2019. Contains 320328 sequences. (Running on oeis4.)